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For a charged particle (with charge e) in an electromagnetic field the Hamiltonian can be written...
3. The Pauli Hamiltonian The Hamiltonian of an electron of mass m, charge q, spinn σ(ox,...
3. The Pauli Hamiltonian The Hamiltonian of an electron of mass m, charge q, spinn σ(ox, σ" σ Pauli matrices), placed in an electromagnetic field described by the vector poten tial A(r, /) and the scalar potential U(r, /). is written: qh 2m The last term represents the interaction between the spin magnetic moment _ơ and the magnetic field B(R, ) - Vx A(R. 1). also be written in the following form ("the Pauli Hamiltonian"): Show, using the properties of...
The page below is equation 3.108 2.2.6 The Lagrangian for a particle with charge q in...
The page below is equation
3.108
2.2.6 The Lagrangian for a particle with charge q in an electromagnetic field described by scalar potential φ and vector potential A is Find the equation of motion of the charged particle. Hint. (d/dt) Aj = aA7/ar + Σ (aA7 /axi )xi. The dependence of the force fields E and B on the potentials ф and A is developed in Section 3.9; see in particular Eq. (3.108).
The force on a charged particle moving in a magnetic field can be computed as the...
The force on a charged particle moving in a magnetic field can be computed as the vector sum of the forces due to each separate component of the magnetic field. As an example, a particle with charge q is moving with speed v in the? y-direction. It is moving in a uniform magnetic field Part A What is the x-component of the force F? exerted on the particle by the magnetic field? Part B What is the y-component of the force...
T/F No matter how complicated the motion of a charged particle in a uniform magnetic field...
T/F No matter how complicated the motion of a charged particle in a uniform magnetic field the component of the velocity parallel to the field remains CONSTANT T/F The magnetic force cannot accelerate a single charged particle A particle with a speed v = 1.5 times 10^5 m/s moves 30 degree relative to the magnetic field (see the image at the right). The magnitude of the magnetic 30 field is B = 2T. What is the magnetic force on the...
3. The Hamiltonian of a particle of mass m and charge q in a static magnetic field may be written 2 where πί Pi-qAi(x). We shall assume that the magnetic field B is uniform, so that AiEijkBjxk is a s...
3. The Hamiltonian of a particle of mass m and charge q in a static magnetic field may be written 2 where πί Pi-qAi(x). We shall assume that the magnetic field B is uniform, so that AiEijkBjxk is a suitable choice. (a) Find Hamilton's equation of motion for the particle. (Hint: To simplify the algebra, use the chain rule to write9and similarly for p) 8H UT, 0z,, and similarly for Sp use the chain rule to write oz (b) Show...
Interactive Exercises 22.14: Motion of a Charged Particle in an External Electric Field I A particle...
Interactive Exercises 22.14: Motion of a Charged Particle in an External Electric Field I A particle has mass 10.0 g and charge of magnitude l 1.00 mC. You do not know the sign of the particle's cherge. The particle moves in the horizcntal xy plene. (You carn ignore the effects of the force due to gravity on the partice.) The partide is projected from the rigin with initial velocity V witn components ex d oy that you can adjust-see the...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
need ans for the following questions, the last 3 pages for more info. Questions: more info:...
need ans for the following questions, the last 3 pages for more
info.
Questions:
more info:
expermint e/m avr=1.71033*10^11
7 2 points of the following options, which conditions for V or I produce the largest radius of the electron beam path r? Hint: Use e/m= 2V (5/4)*aP/(Nuo Ir) Maximum land Maximum V O Maximum land Minimum V Minimum I and Maximum V Minimum I and Minimum V 8 2 points By what factor will change if the radius of the...
3. The Pauli Hamiltonian The Hamiltonian of an electron of mass m, charge q, spinn σ(ox, σ" σ Pauli matrices), placed in an electromagnetic field described by the vector poten tial A(r, /) and the scalar potential U(r, /). is written: qh 2m The last term represents the interaction between the spin magnetic moment _ơ and the magnetic field B(R, ) - Vx A(R. 1). also be written in the following form ("the Pauli Hamiltonian"): Show, using the properties of...
The page below is equation
3.108
2.2.6 The Lagrangian for a particle with charge q in an electromagnetic field described by scalar potential φ and vector potential A is Find the equation of motion of the charged particle. Hint. (d/dt) Aj = aA7/ar + Σ (aA7 /axi )xi. The dependence of the force fields E and B on the potentials ф and A is developed in Section 3.9; see in particular Eq. (3.108).
T/F No matter how complicated the motion of a charged particle in a uniform magnetic field the component of the velocity parallel to the field remains CONSTANT T/F The magnetic force cannot accelerate a single charged particle A particle with a speed v = 1.5 times 10^5 m/s moves 30 degree relative to the magnetic field (see the image at the right). The magnitude of the magnetic 30 field is B = 2T. What is the magnetic force on the...
3. The Hamiltonian of a particle of mass m and charge q in a static magnetic field may be written 2 where πί Pi-qAi(x). We shall assume that the magnetic field B is uniform, so that AiEijkBjxk is a suitable choice. (a) Find Hamilton's equation of motion for the particle. (Hint: To simplify the algebra, use the chain rule to write9and similarly for p) 8H UT, 0z,, and similarly for Sp use the chain rule to write oz (b) Show...
Interactive Exercises 22.14: Motion of a Charged Particle in an External Electric Field I A particle has mass 10.0 g and charge of magnitude l 1.00 mC. You do not know the sign of the particle's cherge. The particle moves in the horizcntal xy plene. (You carn ignore the effects of the force due to gravity on the partice.) The partide is projected from the rigin with initial velocity V witn components ex d oy that you can adjust-see the...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
need ans for the following questions, the last 3 pages for more
info.
Questions:
more info:
expermint e/m avr=1.71033*10^11
7 2 points of the following options, which conditions for V or I produce the largest radius of the electron beam path r? Hint: Use e/m= 2V (5/4)*aP/(Nuo Ir) Maximum land Maximum V O Maximum land Minimum V Minimum I and Maximum V Minimum I and Minimum V 8 2 points By what factor will change if the radius of the...
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